Two trains 70 m and 80 m long respectively, run at the rates of 68 km and 40 km an hour respectively on parallel rails in opposite directions. How long do they take to pass each other ?

Options

A. 5 seconds
B. 10 seconds
C. 12 seconds
D. 6 seconds

Answer

To solve the problem of how long two trains take to pass each other, we can follow these steps:

### Step 1: Determine the lengths of the trains
- Train 1 length = 70 m
- Train 2 length = 80 m

### Step 2: Calculate the total distance to be covered
- Total distance = Length of Train 1 + Length of Train 2
- Total distance = 70 m + 80 m = 150 m

### Step 3: Convert the speeds of the trains from km/h to m/s
- Speed of Train 1 = 68 km/h
- Speed of Train 2 = 40 km/h

To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
- Speed of Train 1 in m/s = \( 68 \times \frac{5}{18} = \frac{340}{18} \approx 18.89 \) m/s
- Speed of Train 2 in m/s = \( 40 \times \frac{5}{18} = \frac{200}{18} \approx 11.11 \) m/s

### Step 4: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, we add their speeds:
- Relative speed = Speed of Train 1 + Speed of Train 2
- Relative speed = 18.89 m/s + 11.11 m/s = 30 m/s

### Step 5: Use the formula for time to cross each other
The formula to calculate time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Distance = 150 m
- Speed = 30 m/s

Now, substituting the values:
- Time = \( \frac{150 \text{ m}}{30 \text{ m/s}} = 5 \text{ seconds} \)

### Final Answer
The time taken for the two trains to pass each other is **5 seconds**.

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